A particle is projected with velocity 
so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as 
, where value of 
is: (Given, ' 
' is the acceleration due to gravity.)
Text Solution
Verified by ExpertsD
Given that the horizontal range of a projectile is three times its maximum height, we need to determine the value of 
in the expression for the range 
.
Let's start by setting up the equations for the range and maximum height of a projectile.
The formula for the range 
is:
The formula for the maximum height 
is:
According to the problem, the range 
is three times the maximum height 
:
Substituting the formulas for 
and 
into this condition gives:
Simplifying this equation, we get:
Using the identity 
, we can rewrite:
This gives us:
Dividing both sides by 
, assuming 
, we have:
Rearranging the terms to solve for 
, we get:
Thus, the angle 
where 
corresponds to 
.
Now, substituting back into the range formula:
The calculation yields:
Therefore, the value of 
in the expression 
is 
.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems